To Nicolás Stier, whose research focuses on network design, traffic jams are a sign of a network gone wrong. Consider a congested metropolis like New York. Stier judges a city’s transportation network on its average commuting time, which is a way of measuring how well the transportation system works. The system is considered equitable if it isn’t structured to give unfair advantages to one socioeconomic class — for example, providing short, cheap commutes for the rich but few affordable options for the poor.

In most major cities, people can choose either to drive or take public transportation to work. Commuters select the option that works best for them based on a combination of travel time and cost (for example, many prefer the option that requires the least travel time, even though taking the subway, bus or commuter train may be less comfortable than driving one’s car). In urban networks, roads are in high demand, and the choices made by each person affect the choices that others will make. When too many commuters decide to drive, congestion increases sharply. For this reason, having relatively few people switch to other modes will significantly improve the commute time of an average resident.

To influence drivers to opt for public transportation, municipal governments can offer incentives, such as subsidies or discounts for using the subway, or create disincentives for commuting by car, such as higher taxes and fees. Subsidies decrease the costs of the poor, who are price sensitive, and decrease the commute time of the rich who are time sensitive, thus improving everybody’s welfare. In addition, subsidies are the more politic approach, since they don’t increase costs; that’s why most major cities subsidize subways, while only a handful have tried congestion pricing.

Cities encourage commuters to use mass transit to achieve a variety of objectives, such as reducing congestion and pollution, which not only benefits the environment but also helps businesses to operate more efficiently (thereby generating more tax dollars). That’s another reason public transportation systems are often heavily subsidized. “Even with the recent fare increases in New York, users aren’t paying the real cost of operating the subway,” says Stier. “The subsidies are a way of influencing behavior.”

The problem is figuring out which options should be subsidized, how much they should be subsidized and how to pay for the subsidies. Stier and his research partner, Patrick Maillé of École Nationale Supérieure des Télécommunications de Bretagne in France, developed an optimization model that can be used to compare different pricing schemes and to find the best possible subsidies for all transportation alternatives.

The researchers’ model can be applied to any system in which a central organization can give incentives to influence the choice of an alternative over others. For example, a shipping company that uses planes, trains and trucks to move packages around the world might want to encourage its business units to choose the shipping option that maximizes profits on a corporate level. Or a government agency could impose price controls on contracts offered by network providers (and compensate them) to increase the efficiency of telecommunications networks.

“In a company that is not tightly integrated,” Stier says, “business units may seek to maximize their own profits, just like every commuter in a city wants to have the shortest commute possible. But the management can offer rebates to align the incentives of the unit to those of the corporation as a whole.”

Ideally, he says, an incentive policy should be structured to at least partially fund itself. In the case of a city managing its transportation network, the subsidies should produce an economic benefit. “If a city subsidizes mass transit, more people will choose that option,” Stier says. “That will reduce the average commute time among travelers and also reduce traffic jams for those who continue to drive.” Everyone will spend less time getting to work, businesses will operate more efficiently and will pay more taxes and the city can use this money to offset some of the cost of the subsidies. “It enables the city to increase its social welfare.”

Nicolás Stieris assistant professor of decision, risk and operations at Columbia Business School.

Nicolás Stier-Moses

Nicolás Stier-Moses was a Columbia Business School faculty member from 2004 to 2013.

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